yes, but it's the same algorithm

yes but i'm asking about what you were really trying to say - are you trying to say one can generate these textures by specifying a filter (transfer function or whatever you want to call it) with a random phase component? and then take ifft to get the definition in space?

If I understand this correctly, it's not even a matter of using a filter, just a case of summing some random sinusoids with an appropriate weighting for each according to the frequency. You can do this by starting off with noise in the frequency domain and shaping it before doing an iFFT.

Yes, I meant exactly that. You build a spectrum by setting the amplitudes to the desired decay law, and the phases to random. It is an octave/matlab one-liner.